OPTIMAL TRANSFER PROGRAMS:
TARGETING, TAGGING, AND ORDEALS
Henrik Jacobsen Kleven
London School of Economics
Lecture Notes for MSc Public Economics (Ec426): Lent term 2009
AGENDA
1. The different types of social programs.
2. The moral hazard cost of low-income support.
3. Reducing moral hazard through better targeting:
(a) Tagging [Akerlof, AER 1978]
(b) In-kind benefits, goods subsidies [Nichols-Zeckhauser, AER 1982]
(c) Ordeals [Nichols-Zeckhauser, AER 1982; Besley-Coate, AER 1992]
4. Lessons from U.S. welfare reform efforts.
TYPES OF SOCIAL PROGRAMS:
WHO HAVE ACCESS?
Universal programs: equal access to benefits for all citizens.
Means-tested programs: access is restricted by income and assets.
Categorical programs: access restricted by personal characteristics
(kids, marital status, immigration status, disability, old age).
Many programs are both means-tested and categorical, e.g. programs
targeted to low-income single mothers (e.g., TANF in the US).
TYPES OF SOCIAL PROGRAMS:
WHAT KIND OF BENEFIT?
Cash programs: provide cash benefits (e.g., TANF in the US).
In-kind programs: provide goods such as health care (e.g., Medicaid
in the US), food (e.g., Food Stamps in the US) and housing.
The principle of consumer sovereignty seems to suggest that cash is
always better than goods.
But this argument may be wrong. To see why, we have to consider the
moral hazard cost–or efficiency cost–of social programs.
A MEANS-TESTED CASH PROGRAM
A typical means-tested cash program provides benefits
½
G − t · wh wh ≤ G/t
B=
0
wh > G/t
where G is an income guarantee, t is a phase-out rate, wh is earnings.
If t = 1, the program brings everyone below the G-level (e.g. the poverty
line) up to G, but provides no support above G.
In the phase-out range wh ≤ G/t, the individual budget constraint is
c ≤ wh + B
⇔
c ≤ (1 − t) wh + G
The benefit phase-out works like a tax. The benefit scheme gives an
incentive to reduce labor supply so as to qualify for a higher benefit.
LABOR SUPPLY RESPONSES TO A
MEANS-TESTED WELFARE PROGRAM
consumption c
rich guy
slope w2
slope w1
middle-class guy
slope w0
poor guy
hours worked h
LABOR SUPPLY RESPONSES TO A
MEANS-TESTED WELFARE PROGRAM
u2
consumption c
rich guy
w2h2
slope w2
slope w1
u1
middle-class guy
u0
slope w0
poor guy
w1h1
w0h0
h0
h1
h2
hours worked h
LABOR SUPPLY RESPONSES TO A
MEANS-TESTED WELFARE PROGRAM
u2
consumption c
rich guy
w2h2
slope w2
slope w1
u1
middle-class guy
u0
slope w0
poor guy
w1h1
poverty line
w0h0
h0
h1
h2
hours worked h
LABOR SUPPLY RESPONSES TO A
MEANS-TESTED WELFARE PROGRAM
u2
consumption c
rich guy
w2h2
slope w2
slope w1
u1
middle-class guy
u0
slope w0
poor guy
w1h1
G
w0h0
poverty line = income guarantee
(phase-out t = 1)
h0
h1
h2
hours worked h
OKUN’S LEAKY BUCKET AND MORAL HAZARD
The income redistribution process is like a leaky bucket: we are carrying
money from the rich to the poor, but some of the money leaks out.
Two types of moral hazard create the leak:
1. The not-so-poor masquerade as poor to qualify for higher benefits
→ make social programs more expensive.
2. The rich masquerade as not-so-rich to avoid some of the income tax
→ reduce revenue for social programs
These revenue leaks imply that a redistributive tax-transfer scheme imposing a 1$ cost on the rich will be able to give less than $1 to the poor.
The difference is the moral hazard cost.
THE INFORMATIONAL CONSTRAINT
A first-best benefit scheme would be based on earnings capacity /
ability (w) which is immutable for the individual.
But w is known only to the individual–the gov’t observes earnings wh
(asymmetric information).
Because earnings is a choice variable, an earnings-based welfare program
induces high-ability individuals to reduce earnings and masquerade as
low-ability individuals. Hence, the program is only second-best.
How can we better target truly low-ability individuals given the informational constraint?
INCREASING TARGET EFFICIENCY
1. Move from earnings-based to categorical programs (tagging).
[Akerlof, AER 1978].
2. Move from cash to in-kind programs and goods subsidies.
[Nichols & Zeckhauser, AER 1982].
3. Use ordeal mechanisms (pure deadweight costs on recipients).
[Nichols & Zeckhauser, AER 1982; Besley & Coate, AER 1992].
TAGGING
If we can identify individual characteristics that are
1. observable to the government
2. negatively correlated with earnings capacity
3. immutable for the individual (unresponsive to incentives)
then targeting benefits to such characteristics is optimal.
Criteria 1 makes this form of targeting feasible, criteria 2 ensures that it
redistributes from high- to low-ability, and criteria 3 ensures that there
is no moral hazard associated with this redistribution.
AN AKERLOF-TYPE MODEL
A population consists of individuals with identical preferences and heterogeneous abilities (= wage rates) w.
A share γ of the population–group A–are (visibly) disabled and have
w = 0.
The remaining share–group B–are not (visibly) disabled. This group
is distributed on (w, w̄) according to density f (w).
The gov’t cannot observe the ws directly, but it can observe type-A
disability.
AN AKERLOF-TYPE MODEL
The gov’t operates a Negative Income Tax (NIT) system giving a lump
sum transfer G financed by a constant marginal tax rate t. The transfer
can potentially be targeted according to disability, i.e. G = {GA, GB }.
We assume a quasi-linear utility function
u = (1 − t) wh + G − d (h) ,
where h is hours worked, and disutility of working d (h) is an increasing,
convex function (d0 > 0, d00 > 0) normalized so that d (0) = 0.
INDIVIDUAL OPTIMIZATION
Optimal labor supply is characterized by
d0 (h) = (1 − t) w if d0 (0) ≤ (1 − t) w; otherwise h = 0.
Group A have w = 0 and hence choose the corner solution hA = 0
giving indirect utility vA = GA.
Group B choose hB = hB ((1 − t) w) ≥ 0 giving indirect utility vB =
(1 − t) whB + GB − d (hB ).
GOVERNMENT OPTIMIZATION
A system with GA = GB is universal, whereas a system with GA 6= GB
is categorical (tagging).
The gov’t chooses GA, GB and t to maximize social welfare
Z w̄
W = γΨ (vA) + (1 − γ)
Ψ (vB ) f (w) dw
w
subject to a gov’t budget constraint
Z w̄
(1 − γ)
twhB f (w) dw − γGA − (1 − γ) GB = 0.
w
The Lagrange multiplier associated with the gov’t budget is λ.
OPTIMAL TRANSFER POLICY
The FOC for GA is given by
γΨ0 (GA) − γλ = 0.
The FOC for GB is given by
Z w̄
(1 − γ)
Ψ0 (vB ) f (w) dw − (1 − γ) λ = 0.
w
Hence, the optimal policy satisfies
Z w̄
Ψ0 (GA) =
Ψ0 (vB ) f (w) dw.
w
THE OPTIMALITY OF TAGGING
We have vB > GB for those with hB > 0 (revealed preference). Since
Ψ (.) is strictly concave, we then have Ψ0 (vB ) < Ψ0 (GB ). (For those
with hB = 0, we have vB = GB and Ψ0 (vB ) = Ψ0 (GB )). Then,
Ψ0 (GA) =
Z w̄
w
Ψ0 (vB ) f (w) dw < Ψ0 (GB ) .
This inequality can only be satisfied by having GA > GB .
Universal benefits (GA = GB ) are dominated by categorical benefits to
the disabled (GA > GB ).
THE OPTIMAL MARGINAL TAX RATE
The FOC for t can be written as
¡ 0
¢
1 cov Ψ (vB ) , wh
t
=− ·
> 0,
1−t
λ
ε · E [wh|B]
where E [wh|B] denotes average earnings in group B and ε is the labor
supply elasticity.
¡ 0
¢
The covariance cov Ψ (vB ) , wh is always negative, since wh is increasing in w, vB is increasing in w, and Ψ (.) is concave.
The numerator reflects preferences for equality. The denominator reflects the concern for efficiency.
TAGGING IN PRACTICE
We have a theoretical case for targeting benefits according to individuals
characteristics that are (1) observable, (2) negatively correlated with
earnings capacity, and (3) immutable.
But are there characteristics satisfying all three criteria in practice?
Potential candidates: (a) blindness and disability, (b) single motherhood.
Single motherhood is widely used as a tagging device in many countries.
It satisfies 1 and 2, but does it satisfy 3? It has been accused by
conservatives of destroying the stable family.
IS SINGLE MOTHERHOOD CAUSED
BY WELFARE INCENTIVES?
Evidence suggests that the effect is either very small or non-existent:
1. U.S. time series evidence shows that single motherhood has been
increasing since the 70s, whereas welfare benefits have been declining.
But it is difficult to draw causal interpretations from time series.
2. U.S. state/time variation in welfare benefits and single motherhood. Single motherhood does not grow (significantly) more in states
that are raising benefits relative to others (Moffitt, JEL 1992; Blank,
JEL 2002).
WELFARE BENEFITS AND SINGLE MOTHERHOOD
OVER TIME IN THE UNITED STATES
Source: Gruber (2007)
IS DISABILITY A GOOD TAGGING DEVICE?
Classification errors in social insurance programs:
TYPE I ERROR
a truly eligible individual applies for benefits
but is rejected
TYPE II ERROR
a truly ineligible individual applies for benefits
and is accepted (moral hazard)
Benítez-Silva, Buchinsky, Rust (NBER 2004): for the U.S. DI program,
the type II error rate is 22% and the type I error rate is 62%.
These numbers suggest that neither the observability nor the unchangeability criteria are completely satisfied for DI.
NICHOLS & ZECKHAUSER (1982):
PUTTING RESTRICTIONS ON RECIPIENTS
The idea of tagging is to use observables to identify the least able. An
alternative approach is to set up a system inducing self-revelation.
Nichols and Zeckhauser (1982) analyze ways of inducing self-revelation
through restrictions on recipients.
Restrictions can be placed on (a) the choice of income, (b) the choice
of consumption, or (c) the allocation of time.
The general theme is that such restrictions can improve target efficiency
if they are more costly to imposters than to intended recipients.
A SIMPLE MODEL
Two individuals: high-ability wH and low-ability wL. One common
utility function u (ci, hi) for i = L, H. Consumption ci equals earned
income wihi ≡ yi plus a net transfer.
The gov’t has a concave social welfare function and wishes to redistribute from H to L, but it cannot observe abilities.
The tax-transfer schedule has to be based on income and takes the
following form: if income is less than ȳ, receive transfer T . If income is
greater than ȳ, pay tax T .
INCENTIVE COMPATIBILITY
If the scheme is too generous, H masquerades as L by choosing income
ȳ. In this case, there would be no redistribution, only inefficient choices.
The optimal tax-transfer scheme must satisfy incentive compatibility
µ
¶
µ
¶
∗
yH
ȳ
∗
u yH − T,
≥ u ȳ + T,
(IC)
wH
wH
∗ is the optimal choice of H conditional on not masquerading.
where yH
The optimal tax system redistributes as much as possible, while ensuring that (IC) is satisfied.
OPTIMAL TRANSFER ELIGIBILITY
∗ . This reduces ȳ as far below y ∗ as possible
A natural solution is ȳ = yL
H
(to prevent moral hazard) without hurting L.
But this is not optimal because, from (IC), if we reduce ȳ further, we
relax the incentive compatibility constraint and can increase T .
∗ , the cost to L is second-order but the
As we move ȳ slightly below yL
cost to H (if he masquerades) is first-order. Room to increase T (a
first-order gain for L) without H masquerading.
This income restriction satisfies some productive efficiency to increase
target efficiency.
THE OPTIMALITY OF RESTRICTING RECIPIENTS’ INCOME
utility
uH (get transfer)
uH*
first-order
utility loss
uH (pay tax)
uL*
second-order
utility loss
uL
y ‘ yL* = y
yH*
pre-tax income
IN-KIND BENEFITS AND GOODS SUBSIDIES
Can target efficiency be improved further by restricting other choices
than income? What about restricting consumption choices by linking
redistribution to specific goods?
There is a strong a priori argument against doing this: consumer sovereignty. The utility gain from receiving a bundle of goods is never
higher than the cash value of those goods.
But, although this argument applies to each recipient individually, it
may not apply for a program as a whole.
EXTENDING THE MODEL
Allow for two consumption goods, x and z, the prices of which are px
and pz .
The utility function is u (xi, zi, hi, wi) for i = L, H. We allow for ability
to impact utility directly.
The tax-transfer schedule imposes a tax T above income ȳ and gives a
transfer T at or below ȳ.
∗ and
This system has been optimized as prescribed above, i.e. ȳ < yL
H marginally prefers not to masquerade.
DEMAND IF MASQUERADING
If H³masquerades, his´budget is pxxH + pz zH = ȳ + T and his utility
is u xH , zH , wȳ , wH . Utility is maximized under the budget with
H
respect to xH and zH .
³
´
Optimal demand for x is then x∗H = xH px, pz , ȳ + T, wȳ , wH .
H
³
´
For the low-ability individual, we have x∗L = xL px, pz , ȳ + T, wȳ , wL .
L
Demand for x (and z) may depend on ability either through the argument wȳ (substitutability with leisure) or through the argument wi
i
(direct preference-dependence on ability).
OPTIMALITY OF IN-KIND TRANSFER
If x∗L > x∗H , so that demand varies with ability conditional on income,
then x is an indicator good.
If such a good exists, we can improve target efficiency by linking redistribution to this good. The argument is a first-order vs second-order
argument as before.
If we convert part of the cash transfer into a transfer of x at a level
slightly above x∗L, we hurt L a little bit but we hurt H more (if he
masquerades). Room to increase T (a first-order gain for L) without H
masquerading.
THE OPTIMALITY OF IN-KIND TRANSFERS
utility
uH (xH*)
uH (xL*)
uL*
uL
uH (masquerade)
xH*
xL*
quantity of x
THE OPTIMALITY OF IN-KIND TRANSFERS
utility
uH (xH*)
first-order
utility loss
uH (xL*)
uL*
second-order
utility loss
uL
uH (masquerade)
xH*
xL*
quantity of x
WHEN CAN IN-KIND BENEFITS AND SUBSIDIES
IMPROVE TARGET EFFICIENCY?
1. If differences in demand across rich and poor are due only to income
effects (luxuries versus necessities), in-kind transfers cannot improve
target efficiency.
2. If, conditional on income, demand varies with ability, in-kind transfers can improve target efficiency.
Potential candidates: housing projects, medical care.
ORDEALS
An ordeal is a pure deadweight cost on recipients.
Examples of ordeals are:
1. Work and training requirements (workfare). Used in U.S. TANF.
2. Tedious and complex administrative procedures. Common in many
social programs (Currie, 2004).
3. Demeaning qualification tests.
4. In-hospital requirements in health insurance. Used in U.S. Medicaid.
ORDEALS, CONT’D
Ordeals can serve a screening function if (i) the utility gain from transfers is lower for the non-deserving, and/or if (ii) the utility cost of the
ordeal is higher for the non-deserving.
Two types of recipients in a cash welfare program: low-ability individuals and high-ability but "lazy" individuals.
Introduce a time loss in the program, e.g. work requirements or waiting lines. The time loss will be more costly to the high-ability/lazy
individuals.
THE COST OF ORDEALS: INCOMPLETE TAKE UP
A problem with many social programs, especially in the U.S., is that
not all eligibles take up benefits. Take-up rates can be far lower than
100% in some programs.
Three possible explanations: (i) welfare stigma, (ii) imperfect information, (iii) transaction costs associated with take up.
The third explanation is related to the presence of ordeals. Currie
(2004) suggests that transaction costs due to ordeals may be an empirically important factor for incomplete take up.
U.S. WELFARE REFORM
The Personal Responsibility and Work Opportunity Reconciliation Act
of 1996 (PRWORA), or the welfare reform law:
1. Cash welfare was changed from matching grants to lump-sum block
grants from the federal gov’t to state gov’ts.
2. States were given greater discretion in designing programs.
3. Work requirements were imposed on welfare recipients.
4. Time limits were imposed on welfare recipients.
5. New efforts to limit unwed motherhood were introduced.
WELFARE CASELOADS OVER TIME IN THE U.S.
Source: Gruber (2007)
THE IMPACT OF WELFARE REFORM: TIME SERIES
Over the 1990s, caseloads fell, labor force participation soared, and the
poverty rate declined. But time series evidence is not compelling:
1. The caseload fall began in 1994 (and the participation increase even
earlier), i.e. before the welfare reform took effect.
2. The 1990s saw one of the largest economic booms in the U.S. history.
3. The welfare reform was passed shortly after two tax reform acts (1990
and 1993) which also aimed at bringing low-income single mothers
into work through expansions of the EITC.
It is very difficult to separate the effects from welfare reform, tax reform,
and the business cycle.
QUASI-EXPERIMENTAL ESTIMATIONS
Use the reform as a natural experiment by comparing a treatment group
T affected by the reform to a control group C not (or less) affected, but
experiencing similar macro economic shocks. Two possibilities:
1. Compare single mothers (T ) to either married mothers (C1) or single
women without children (C2).
2. Use the fact that some states (but not others) were allowed to experiment with certain aspects of the reform before the national law
was in place.
These approaches suggest that the welfare reform did have positive
effects, but was far from the whole story (see Blank, JEL 2002).